Urn A contains 2 white, 1 black and 3 red balls, urn B contains 3 white, 2 black and 4 red balls and urn C contains 4 white, 3 black and 2 red balls. One urn is chosen at random and 2 balls are drawn at random from the urn. If the chosen balls happen to be red and black, what is the probability that both balls come from urn B?

Explanation

To solve the problem, we need to find the probability that both balls drawn are from urn B given that one ball is red and the other is black. We will use Bayes' theorem for this calculation.

### Step 1: Define Events
Let:
- \( E_1 \): The event that one ball is red and one ball is black.
- \( E_2 \): The event that both balls are from urn B.

We want to find \( P(E_2 | E_1) \).
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